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AP Statistics Linear Regression and Correlation — practice questions

Explore 21 free Linear Regression and Correlation questions in AP Statistics Statistics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Regression and Correlation questions and exercises with answers

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In the linear equation y = a + bx, the letter b represents the:Read the answer and worked solution →In the linear equation y = a + bx, the letter a represents the:Read the answer and worked solution →The display used to show the relation between two variables x and y is a:Read the answer and worked solution →The line fitted through a scatter plot by regression is called the line of best fit or the:Read the answer and worked solution →The difference between an observed y value and the value predicted by the line is called the:Read the answer and worked solution →In simple linear regression, how many independent variables are used?Read the answer and worked solution →Points of the fitted line are written with which notation for the predicted value?Read the answer and worked solution →A residuals plot done correctly should appear:Read the answer and worked solution →A pattern left in a residuals plot suggests that:Read the answer and worked solution →Alongside the line itself, the other quantity calculated and interpreted in this analysis is the:Read the answer and worked solution →A scatter plot of data suited to linear regression should resemble:Read the answer and worked solution →The scatter plot and the residuals plot are read differently: the scatter plot should look linear while the residuals plot should look:Read the answer and worked solution →The error term for a single data point is written as the observed y minus the:Read the answer and worked solution →Least-squares regression earns its name because the fitting rule minimises the sum of the squared:Read the answer and worked solution →An outlier in a regression analysis shows up in a residuals plot as a point that is:Read the answer and worked solution →Interpreting the slope b in a fitted line means reading it as the change in y for:Read the answer and worked solution →Match each regression termRead the answer and worked solution →Scatter plot or residuals plot?Read the answer and worked solution →True or false: regressionRead the answer and worked solution →Fit a regression line in orderRead the answer and worked solution →Complete the regression rulesRead the answer and worked solution →

Worked practice questions

In the linear equation y = a + bx, the letter b represents the:

  1. The slope
  2. Y-intercept
  3. X-intercept
  4. A residual
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Correct answer: A. The slope

1. A straight line is fixed by where it starts and how steeply it rises. 2. For the linear equation y = a + bx, b is the slope and a is the y-intercept. 3. The slope reports the change in y for a one-unit change in x. 4. The intercept is the value of y when x is zero. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 12 'Linear Regression and Correlation', sections 12.1-12.6_

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In the linear equation y = a + bx, the letter a represents the:

  1. A residual
  2. Y-intercept
  3. The slope
  4. Correlation
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Correct answer: B. Y-intercept

1. The two coefficients of a straight line play different roles. 2. For the linear equation y = a + bx, b is the slope and a is the y-intercept. 3. The y-intercept is where the line crosses the vertical axis. 4. Confusing it with the slope is the standard error here. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 12 'Linear Regression and Correlation', sections 12.1-12.6_

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The display used to show the relation between two variables x and y is a:

  1. A histogram
  2. The pie chart
  3. Scatter plot
  4. The box plot
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Correct answer: C. Scatter plot

1. Before fitting anything, you look at the two variables together. 2. Before taking up the discussion of linear regression and correlation, we need to examine a way to display the relation between two variables x and y. 3. That display is the scatter plot. 4. Box plots, histograms and pie charts each show one variable at a time. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 12 'Linear Regression and Correlation', sections 12.1-12.6_

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